X-ray imaging technology provides a non-invasive technique of visualizing the internal structure of an object of interest by exposing the object to high energy electromagnetic radiation (i.e., X-rays). X-rays emitted from a radiation source pass through the object and are absorbed at varying levels by the internal structures of the object. As a result, X-ray radiation exiting the object is attenuated according to the various absorption characteristics of the materials which the X-rays encounter. By measuring the attenuation of the X-ray radiation that exits the object, information related to the density distribution of the object may be obtained.
To obtain X-ray information about an object, an X-ray source and an array of detectors responsive to X-ray radiation may be arranged about the object. Each detector in the array, for example, may generate an electrical signal proportional to the intensity of X-ray radiation impinging on a surface of the detector. The source and array may be rotated around the object in a circular path to obtain a number of views of the object at different angles. At each view, the detector signal generated by each detector in the array indicates the total absorption (i.e., attenuation) incurred by material substantially in a line between the X-ray source and the detector. Therefore, the array of detection signals records the projection of the object onto the detector array at a number of views of the object, and provides one method of obtaining view data of the object.
View data obtained from an X-ray scanning device may be of any form that provides attenuation information (e.g., detector outputs) as a function of view angle or orientation with respect to the object being imaged. View data may be obtained by exposing a planar cross-section of the object, referred to as a slice, to X-ray radiation. Each rotation about the object (e.g., a 180 degree rotation of the radiation source and detector array) provides attenuation information about a two-dimensional (2D) slice of the object.
Accordingly, the X-ray scanning process transforms a generally unknown density distribution of an object into view data corresponding to the unknown density distribution. FIG. 1A illustrates a diagram of the transformation operation performed by the X-ray scanning process. A 2D cross-section of object 100 having an unknown density distribution in object space is subjected to X-ray scanning. Object space refers herein to the coordinate frame of an object of interest, for example, an object undergoing an X-ray scan. A Cartesian coordinate frame (i.e., (x, y, z)) may be a convenient coordinate system for object space, however, object space may be described by any other suitable coordinate frame, such as spherical or cylindrical coordinates.
X-ray scanning process 110 generates object view data 105 in a view space coordinate frame (e.g., coordinate frame (t,θ)). For example, object view data 105 may include attenuation information from a plurality of detectors in an array (corresponding to the view space axis ti), at a number of orientations of the X-ray scanning device (corresponding to the view space axis θi). Accordingly, X-ray scanning process 110 transforms a continuous density distribution in object space to discrete view data in view space.
To generate an image of the 2D density distribution from view data of an object, the view data may be projected back into object space. The process of transforming view data in view space into image data represented in object space is referred to as image reconstruction. FIG. 1B illustrates an image reconstruction process 120 that transforms view data 105 into a 2D image 100′ (e.g., a viewable image of the cross-section of object 100 that was scanned). To form 2D image 100′, a density value for each discrete location of the cross-section of object 100 in object space is determined based on the information available in view data 105.
Many techniques have been developed for image reconstruction to transform acquired view data into image data. For example, filtered back-projection is a widely used technique to form 2D images from view data obtained from an X-ray scanning device. In addition, a number of such 2D images taken across successive slices of an object of interest may be stacked together to form a three dimensional (3D) image. In medical imaging, computed tomography (CT) images may be acquired in this manner.
Images obtained via reconstruction contain less information than the view data from which they were computed. The loss in information is due in part to the discrete nature of X-ray scanning (i.e., a finite number of detectors and a finite number of views) and to assumptions made during back-projection. In this respect, an image represents intensity as a discrete function of space. The term “intensity” refers generally to a magnitude, degree and/or value at some location in the image. To back-project view data, the scan plane (i.e., the 2D cross-section of the object being imaged) may be logically partitioned into a discrete grid of pixel regions.
Each pixel region in object space may be assigned an intensity value from a finite number of integral attenuation measurements taken along rays intersecting the region of space corresponding to the respective pixel region. That is, intensity values are assigned such that the discrete sum of assigned intensities along rays through the grid match the corresponding integral attenuation measurements. This operation assumes that all structure within a pixel region has a same and single density and therefore computes an average of the density values within the corresponding region of space. This averaging blurs the image and affects the resulting image resolution.
When multiple structures are sampled within a single pixel (e.g., when structure within the object is smaller than the dimension of the corresponding pixel region and and/or the boundary of a structure extends partially into an adjacent pixel region), information about the structure is lost. The result is that the reconstructed image data has less resolution than the view data from which it was generated. This loss of resolution may obscure and/or eliminate detail in the reconstructed image.
In conventional medical imaging, a human operator, such as a physician or diagnostician, may visually inspect a reconstructed image to make an assessment, such as detection of a tumor or other pathology or to otherwise characterize the internal structures of a patient. However, this process may be difficult and time consuming. For example, it may be difficult to assess 3D biological structure by attempting to follow 2D structure through a series of stacked 2D images. In particular, it may be perceptually difficult and time consuming to understand how 2D structure is related to 3D structure as it appears, changes in size and shape, and/or disappears in successive 2D image slices. A physician may have to mentally arrange hundreds or more 2D slices into a 3D picture of the anatomy. To further frustrate this process, when anatomical structure of interest is small, the structure may be difficult to discern or absent altogether in the reconstructed image.
Image processing techniques have been developed to automate or partially automate the task of understanding and partitioning the structure in an image and are employed in computer aided diagnosis (CAD) to assist a physician in identifying and locating structure of interest in a 2D or 3D image. CAD techniques often involve segmenting the image into groups of related pixels and identifying the various groups of pixels, for example, as those comprising a tumor or a vessel or some other structure of interest. However, segmentation on reconstructed images has proven difficult and Applicant has appreciated that it may be ineffective in detecting small structures whose features have been obscured or eliminated during image reconstruction.
Reconstructed images of view data obtained from conventional X-ray scanning devices may be limited to a resolution of approximately 500 microns. As a result, conventional imaging techniques may be unable to image structure having dimensions smaller than 500 microns. That is, variation in the density distribution of these small structures cannot be resolved by conventional image reconstruction. Micro-computer tomography (microCT) can produce view data of small objects at resolutions that are an order of magnitude greater than conventional X-ray scanning devices. However, microCT cannot image large objects such as a human patient and therefore is unavailable for in situ imaging of the human anatomy.
Model-based techniques have been employed to avoid some of the problems associated with image reconstruction and post-reconstruction image processing algorithms. Model-based techniques may include generating a model to describe structure assumed to be present in the view data of an object of interest. For example, a priori knowledge of the internal structure of an object of interest may be used to generate the model. The term “model” refers herein to any geometric, parametric or other mathematical description and/or definition of properties and/or characteristics of a structure, physical object, or system. For example, in an X-ray environment, a model of structure may include a mathematical description of the structure's shape and density distribution. A model may include one or more parameters that are allowed to vary over a range of values, such that the model may be deformed to take on a variety of configurations. The term “configuration” with respect to a model refers herein to an instance wherein each of the model parameters has been assigned a particular value.
Once a configuration of a model is determined, view data of the model (referred to as model view data) may be computed, for example, by taking the radon transform of the model. The radon transform, operating on a function, projects the function into view space. FIG. 1C illustrates the operation of the radon transform 130 on a model 125 of object 100. Model 125 is described by the function ƒ(Φ) in model space, where Φ is a vector of the parameters characterizing the model. Since model 125 is generated to describe object 100, it may be convenient to use the same coordinate frame for model space and object space, although they may be different so long as the transformation between the two coordinate frames are known. The radon transform 130 transforms model 125 from model space to model view data 105′ (i.e., to a function {tilde over (g)}i in the view space coordinate frame).
It should be appreciated that X-ray scanning process 110 and radon transform 130 perform substantially the same operation, i.e., both perform a transformation from object space (or model space) to view space. The scanning process performs a discrete transformation from object space to view space (i.e., to a discrete function in (θi,ti)) and the radon transform performs a continuous transformation from object space to view space (i.e., to a continuous function in (θ,t)). Model view data obtained by projecting a configuration of the model (i.e., an instance of ƒ where each parameter in Φ has been assigned a value) into view space via the radon transform, may then be compared to the object view data acquired from the X-ray scanning device to measure how accurately the model describes the structure of interest in the object being scanned. The model may then be deformed or otherwise updated until its radon transform (the model view data) satisfactorily fits the object view data, i.e., until the configuration of the model has been optimized. The optimization may be formulated, for example, by assuming that the observed object view data arose from structure that is parameterized as the model and finding the parameterization that best describes the object view data. For example, model deformation may be guided by minimizing the expression:E(Φ)=∫N(gi(t,θ;Φ)−{tilde over (g)}i(t,θ;Φ))2dtdθ  (1)
where Φ is a vector of the model parameters, gi represents the object view data and {tilde over (g)}i represents the model view data. That is, the configuration of the model may be optimized by solving for the vector Φ that minimizes E (i.e., by finding the least squares distance).
Applicant has appreciated that when the structure being modeled is complex and includes a number of deformable parameters, the combinatorial problem of configuring the model may become intractable. That is, as the number of parameters over which the model is allowed to vary increases, the number of possible configurations of the model tends to explode. In addition, Applicant has appreciated that with no guidance on how to initially configure the model, a poorly chosen initial hypothesis may cause a subsequent optimization scheme to converge to an undesirable local minimum. As a result, the selected model configuration may poorly reflect the actual structure that was scanned.